Hello
Can you help me
It is reported that 72% of working women use computers at work , choose 4 working wonen at random . Find the probability that :
A : all 4 use a computer at their work
B : at least one does not use a computer at work Please help me 😞
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
A .72^4 = ?
Either-or probabilities are found by adding the individual probabilities.
B. This is saying P of either none using, 3 not using, 2 not using or 1 not using.
P = .28^4 + .28^3*.72… etc.
Of course, I'm here to help!
To find the probability in each case, we need to use the concept of probability and combinations.
A) Probability that all 4 working women use a computer at their work:
For each woman, the probability of using a computer is 72%, which means the probability of not using a computer is 28%. Since these events are independent (the use of computers by one woman does not affect the use by another woman), we can simply multiply the probabilities:
P(all 4 use a computer) = P(use) * P(use) * P(use) * P(use)
= (0.72) * (0.72) * (0.72) * (0.72)
= 0.72^4
≈ 0.2359
So, the probability that all four working women use a computer at their work is approximately 0.2359.
B) Probability that at least one working woman does not use a computer at work:
To find this probability, we need to calculate the complement probability, which is the probability that none of the women use a computer. Once we have that, we can subtract it from 1 to find the probability of at least one woman not using a computer.
P(none use a computer) = P(not use) * P(not use) * P(not use) * P(not use)
= (0.28) * (0.28) * (0.28) * (0.28)
= 0.28^4
≈ 0.0184
Now, the probability of at least one woman not using a computer is:
P(at least one does not use) = 1 - P(none use a computer)
= 1 - 0.0184
≈ 0.9816
Therefore, the probability that at least one working woman does not use a computer at work is approximately 0.9816.
I hope this helps! Let me know if you have any further questions.